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High Energy Normalized Solutions for the Schrödinger Equations with Exponential Critical Growth ZHANG Xiao-cang, XU Li-ping Chinese Quarterly Journal of Mathematics    2025, 40 (1): 1-19.   DOI: 10.13371/j.cnki.chin.q.j.m.2025.01.001 Abstract （147）      PDF（pc） （417KB）（46）       Knowledge map    Save In this paper, we study high energy normalized solutions for the following Schrödinger equation …… Related Articles | Metrics

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The Varieties of Semi-Conformal Vectors of Rank-One Even Lattice Vertex Operator Algebras CHU Yan-jun, GAO Yi-bo Chinese Quarterly Journal of Mathematics    2025, 40 (1): 36-48.   DOI: 10.13371/j.cnki.chin.q.j.m.2025.01.004 Abstract （116）      PDF（pc） （430KB）（31）       Knowledge map    Save In this paper, we shall study structures of even lattice vertex operator algebras by using the geometry of the varieties of their semi-conformal vectors. We first give the varieties of semi-conformal vectors of a family of vertex operator algebras…… Related Articles | Metrics

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Blow-Up Phenomena for a Non-Homogeneously Strongly Damped Wave Equation with Riemann-Liouville Fractional Integral XIANG Chang-yong, DUAN Ji-song, LONG Qun-fei Chinese Quarterly Journal of Mathematics    2025, 40 (3): 304-312.   DOI: 10.13371/j.cnki.chin.q.j.m.2025.03.006 Abstract （115）      PDF（pc） （354KB）（44）       Knowledge map    Save We investigate the blow-up effect of solutions for a non-homogeneous wave equation utt −∆u−∆ut =I0α+ (|u|p)+ω(x), where p >1, 0≤α<1 and ω(x) with \int_{\mathbb{R}^{N}} ω(x)dx >0. By a way of combining the argument by contradiction with the test function techniques, we prove that not only any non-trivial solution blows up in finite time under 0< α <1, N ≥1 and p >1, but also any non-trivial solution blows up in finite time under α= 0, 2≤ N ≤4 and p being the Strauss exponent. Related Articles | Metrics

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The w-(b,c)-Core Inverse FANG Li, ZHAO Liang Chinese Quarterly Journal of Mathematics    2025, 40 (1): 26-35.   DOI: 10.13371/j.cnki.chin.q.j.m.2025.01.003 Abstract （109）      PDF（pc） （308KB）（66）       Knowledge map    Save We introduce and study a new kind of generalized inverses named w-(b,c)-core inverses, which is a generalization of the (b,c)-core inverse. An example is given to show that w-(b,c)-core inverses need not be (b,c)-core inverses. In addition, the dual version of the w-(b,c)-core inverse is studied. Some results on (b,c)-core inverses and e-(b,c)-core inverses are unified and generalized. Related Articles | Metrics

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ub-Riemannian Limits, Connections with Torsion and the Gauss-Bonnet Theorem for Four Dimensional Twisted BCV Spaces LI Hong-feng, LIU Ke-feng, WANG Yong Chinese Quarterly Journal of Mathematics    2025, 40 (2): 111-134.   DOI: 10.13371/j.cnki.chin.q.j.m.2025.02.001 Abstract （103）      PDF（pc） （367KB）（46）       Knowledge map    Save In this paper, we compute sub-Riemannian limits of some important curvature variants associated with the connection with torsion for four dimensional twisted BCV spaces and derive a Gauss-Bonnet theorem for four dimensional twisted BCV spaces. Related Articles | Metrics

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A High-Order Scalar Auxiliary Variable Approach for Nonlinear Parabolic Integro-Differential Equations YAN Li-na, ZHANG Gen-gen, HUANG Qiong-ao Chinese Quarterly Journal of Mathematics    2025, 40 (3): 262-270.   DOI: 10.13371/j.cnki.chin.q.j.m.2025.03.003 Abstract （102）      PDF（pc） （365KB）（11）       Knowledge map    Save An efficient and accurate scalar auxiliary variable (SAV) scheme for numerically solving nonlinear parabolic integro-differential equation (PIDE) is developed in this paper. The original equation is first transformed into an equivalent system, and the k-order backward differentiation formula (BDFk) and central difference formula are used to discretize the temporal and spatial derivatives, respectively. Different from the traditional discrete method that adopts full implicit or full explicit for the nonlinear integral terms, the proposed scheme is based on the SAV idea and can be treated semi-implicitly, taking into account both accuracy and effectiveness. Numerical results are presented to demonstrate the high-order convergence (up to fourth-order) of the developed schemes and it is computationally efficient in long-time computations. Related Articles | Metrics

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On α-Bloch Functions in Several Complex Variables ZHU Ting, YANG Liu Chinese Quarterly Journal of Mathematics    2025, 40 (1): 93-102.   DOI: 10.13371/j.cnki.chin.q.j.m.2025.01.009 Abstract （74）      PDF（pc） （356KB）（15）       Knowledge map    Save In this paper, we establish characterizations of α-Bloch functions and little α-Bloch functions on the unit ball as well as the unit polydisk of Cm, which generalize and improve results of Aulaskari-Lappan, Minda, Aulaskari-Wulan, and Wu. Some examples are also given to complement our theory. Related Articles | Metrics

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Power Options Pricing under Markov Regime-Switching Two-Factor Stochastic Volatility Jump-Diffusion Model 韩书书, 韦煜明 Chinese Quarterly Journal of Mathematics    2025, 40 (1): 59-73.   DOI: 10.13371/j.cnki.chin.q.j.m.2025.01.006 Abstract （74）      PDF（pc） （558KB）（31）       Knowledge map    Save In this paper, we incorporate Markov regime-switching into a two-factor stochastic volatility jump-diffusion model to enhance the pricing of power options. Furthermore, we assume that the interest rates and the jump intensities of the assets are stochastic. Under the proposed framework, first, we derive the analytical pricing formula for power options by using Fourier transform technique, Esscher transform and characteristic function. Then we provide the efficient approximation to calculate the analytical pricing formula of power options by using the FFT approach and examine the accuracy of the approximation by Monte Carlo simulation. Finally, we provide some sensitivity analysis of the model parameters to power options. Numerical examples show this model is suitable for empirical work in practice. Related Articles | Metrics

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Novel Results on the Multi-Parameters Mittag-Leffler Function PAN Yu-mei, LI Yu-fen, CAI Dong-xin, YAN Xing-jie Chinese Quarterly Journal of Mathematics    2025, 40 (1): 82-92.   DOI: 10.13371/j.cnki.chin.q.j.m.2025.01.008 Abstract （73）      PDF（pc） （328KB）（68）       Knowledge map    Save In this article, the multi-parameters Mittag-Leffler function is studied in detail. As a consequence, a series of novel results such as the integral representation, series representation and Mellin transform to the above function, are obtained. Especially, we associate the multi-parameters Mittag-Leffler function with two special functions which are the generalized Wright hypergeometric and the Fox’s-H functions. Meanwhile, some interesting integral operators and derivative operators of this function, are also discussed Related Articles | Metrics

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Applications of Matrix Equations in Linear Time-Invariant Systems ZHOU Yan-ping, CHEN Yan-ping, ZHANG Juan Chinese Quarterly Journal of Mathematics    2025, 40 (3): 221-237.   DOI: 10.13371/j.cnki.chin.q.j.m.2025.03.001 Abstract （72）      PDF（pc） （337KB）（41）       Knowledge map    Save With the development of science and technology, the design and optimization of control systems are widely applied. This paper focuses on the application of matrix equations in linear time-invariant systems. Taking the inverted pendulum model as an example, the algebraic Riccati equation is used to solve the optimal control problem, and the system performance and stability are achieved by selecting the closed-loop pole and designing the gain matrix. Then, the numerical methods for solving the stochastic algebraic Riccati equations are applied to practical problems, with Newton’s iteration method as the outer iteration and the solution of the mixed-type Lyapunov equations as the inner iteration. Two methods for solving the Lyapunov equations are introduced, providing references for related research. Related Articles | Metrics

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Blow-Up Solutions in a Parabolic Equation with Variable Coefficients and Memory Boundary Flux ZHANF An-lei, LIU Bing-chen Chinese Quarterly Journal of Mathematics    2025, 40 (1): 74-81.   DOI: 10.13371/j.cnki.chin.q.j.m.2025.01.007 Abstract （70）      PDF（pc） （280KB）（16）       Knowledge map    Save This paper deals with a semilinear parabolic problem involving variable coefficients and nonlinear memory boundary conditions. We give the blow-up criteria for all nonnegative nontrivial solutions, which rely on the behavior of the coefficients when time variable tends to positive infinity. Moreover, the global existence of solutions are discussed for non-positive exponents. Related Articles | Metrics

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On the Best Constant in Poincar´e Inequality over Simple Geometric Domains CHEN Hong-ru, MA Gao-chao, ZHANG Bei Chinese Quarterly Journal of Mathematics    2025, 40 (2): 148-157.   DOI: 10.13371/j.cnki.chin.q.j.m.2025.02.003 Abstract （70）      PDF（pc） （410KB）（13）       Knowledge map    Save In this paper, we explicitly establish Poincar´e inequality for 1≤p <∞ over simple geometric domains, such as segment, rectangle, triangle or tetrahedron. We obtain sharper bounds of the constant in Poincar´e inequality and, in particular, the explicit relation between the constant and the geometric characters of the domain. Related Articles | Metrics

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A Note on a Result Due to Sauer and Schweizer WANG Guang-sheng, LI Fei, XU Yan Chinese Quarterly Journal of Mathematics    2025, 40 (1): 20-25.   DOI: 10.13371/j.cnki.chin.q.j.m.2025.01.002 Abstract （68）      PDF（pc） （254KB）（17）       Knowledge map    Save n this paper, we obtain some normality criteria for families of meromorphic functions concering shared values, which extends the related results of Schwick, and SauerSchweizer, and can be viewed as a complement of the related results due to Pang-Zalcman, Xu-Fang. Related Articles | Metrics

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xistence of Solutions for Volterra Singular Integral Equations in the Class of Exponentially Increasing Functions ZHANG Wen-wen, LI Ping-run Chinese Quarterly Journal of Mathematics    2025, 40 (2): 135-147.   DOI: 10.13371/j.cnki.chin.q.j.m.2025.02.002 Abstract （67）      PDF（pc） （320KB）（16）       Knowledge map    Save The goal of this paper is to investigate the theory of Noether solvability for Volterra singular integral equations (VSIEs) with convolution and Cauchy kernels in a more general function class. To obtain the analytic solutions, we transform such equations into boundary value problems with discontinuous coefficients by the properties of Fourier analysis. In view of the analytical Riemann-Hilbert method, the generalized Liouville theorem and Sokhotski-Plemelj formula, we get the uniqueness and existence of solutions for such problems, and study the asymptotic property of solutions at nodes. Therefore, this paper improves the theory of singular integral equations and boundary value problems. Related Articles | Metrics

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Numerical Methods for Boundary Value Problems in Variable Coefficient Ordinary Differential Equations ZHAO Ting-ting, CAI Wei-yun Chinese Quarterly Journal of Mathematics    2025, 40 (3): 295-303.   DOI: 10.13371/j.cnki.chin.q.j.m.2025.03.005 Abstract （67）      PDF（pc） （422KB）（13）       Knowledge map    Save In order to solve the problem of the variable coefficient ordinary differential equation on the bounded domain, the Lagrange interpolation method is used to approximate the exact solution of the equation, and the error between the numerical solution and the exact solution is obtained, and then compared with the error formed by the difference method, it is concluded that the Lagrange interpolation method is more effective in solving the variable coefficient ordinary differential equation. Related Articles | Metrics

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The Gauss Circle Problem Related to the Fourier Coefficients of Cusp Forms CHEN Feng Chinese Quarterly Journal of Mathematics    2025, 40 (3): 313-323.   DOI: 10.13371/j.cnki.chin.q.j.m.2025.03.007 Abstract （65）      PDF（pc） （363KB）（25）       Knowledge map    Save Let f be a Hecke eigenform of even integral weight k for the full modular group SL2(Z). Denote by λf (n) the nth normalized coefficient of f. The sum of Fourier coefficients of cusp form over the quadratic polynomial m2 +n2 is considered, i.e.,... Related Articles | Metrics

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On Wiener Index of Power of Paths and Cycles LIU Sai-hua, LI Xiao-rong Chinese Quarterly Journal of Mathematics    2025, 40 (1): 49-58.   DOI: 10.13371/j.cnki.chin.q.j.m.2025.01.005 Abstract （65）      PDF（pc） （328KB）（14）       Knowledge map    Save The Wiener index of a graph is defined to be the sum of the distances of all pairs of vertices in the graph. The kth power Gk of a graph G is the graph on V (G) and two vertices are adjacent if and only if their distance in G is less or equal to k. In this paper, we computed the Wiener index of the kth power of paths and cycles for any k ≥2. Related Articles | Metrics

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A Novel Property of Generalized Fibonacci Sequence in Grids YANG Zi-xian, BAI Jian-chao Chinese Quarterly Journal of Mathematics    2025, 40 (1): 103-110.   DOI: 10.13371/j.cnki.chin.q.j.m.2025.01.010 Abstract （61）      PDF（pc） （1733KB）（16）       Knowledge map    Save Fibonacci sequence, generated by summing the preceding two terms, is a classical sequence renowned for its elegant properties. In this paper, leveraging properties of generalized Fibonacci sequences and formulas for consecutive sums of equidistant sub-sequences, we investigate the ratio of the sum of numbers along main-diagonal and sub-diagonal of odd-order grids containing generalized Fibonacci sequences. We show that this ratio is solely dependent on the order of the grid, providing a concise and splendid identity. Related Articles | Metrics

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A Posteriori Error Estimate of Multiphysics Discontinuous Galerkin Method for a Poroelasticity#br# GE Zhi-hao, HE Wen-long, MA Meng-xia Chinese Quarterly Journal of Mathematics    2025, 40 (3): 238-261.   DOI: 10.13371/j.cnki.chin.q.j.m.2025.03.002 Abstract （61）      PDF（pc） （1766KB）（12）       Knowledge map    Save In this paper, we design a new error estimator and give a posteriori error analysis for a poroelasticity model. To better overcome “locking phenomenon” on pressure and displacement, we proposed a new error estimators based on multiphysics discontinuous Galerkin method for the poroelasticity model. And we prove the upper and lower bound of the proposed error estimators, which are numerically demonstrated to be computationally very efficient. Finally, we present numerical examples to verify and validate the efficiency of the proposed error estimators, which show that the adaptive scheme can overcome “locking phenomenon” and greatly reduce the computation cost. Related Articles | Metrics

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Moments of Dirichlet L-Functions HUANG Bing-rong, HUANG Jun-hao Chinese Quarterly Journal of Mathematics    2025, 40 (4): 360-371.   DOI: 10.13371/j.cnki.chin.q.j.m.2025.04.003 Abstract （59）      PDF（pc） （346KB）（35）       Knowledge map    Save In this paper, we establish asymptotic formulas for a cubic moment of Dirichlet L-functions restricted to a coset, as well as for a mixed moment of Dirichlet L-functions and twists of GL(2) L-functions along a coset. Our main tool is a power-saving estimate of bilinear forms of hyper-Kloosterman sums due to Kowalski–Michel–Sawin. Related Articles | Metrics